As shown in [1]}, the distance \( ||X - WH||_F\)  is non-increasing under the multiplicative update rules. Applying this to the updated \(W_t,H_t\)  at the iteration \(t\) , we have:
\(||Y_{t-1} - W_{t-1}H_{t-1}|| \ge ||Y_{t-1} - W_{t}H_{t}||.\) 
